Zhongkai Tao
I'm a graduate student at UC Berkeley. I am interested in microlocal analysis. My advisor is Maciej Zworski. My email is ztao@math.berkeley.edu. Here is my CV.
Research
Integral formulas for under/overdetermined partial differential operators via recovery on curves, with Philip Isett, Yuchen Mao and Sung-Jin Oh, in preparation;
Flexibility of maximal asymptotically flat initial data sets, with Yuchen Mao and Sung-Jin Oh, in preparation;
Lossless Strichartz and spectral projection estimates on unbounded manifolds, with Xiaoqi Huang, Christopher Sogge and Zhexing Zhang.
Fragile topology on solid grounds and the Thouless conjecture, with Simon Becker and Mengxuan Yang.
Selberg, Ihara and Berkovich, with Jialun Li, Carlos Matheus and Wenyu Pan.
Dirac cones and magic angles in the Bistritzer--MacDonald TBG Hamiltonian, with Simon Becker, Solomon Quinn, Alexander Watson and Mengxuan Yang.
Spectral gap for surfaces of infinite volume with negative curvature.
Optimal enhanced dissipation for contact Anosov flows, with Maciej Zworski, Nonlinearity, 38(2025), no.4, 045001.
Appendix to Mathematical results on the chiral model of twisted bilayer graphene, with Mengxuan Yang, Journal of Spectral Theory, 14(2024), no.3, 1063–1107.
Appendix to Classically forbidden regions in the chiral model of twisted bilayer graphene, with Maciej Zworski, Probability and Mathematical Physics, 6 (2025), No. 2, 505–546.
Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties, with Yuchen Mao and Sung-Jin Oh.
Counting Pollicott--Ruelle resonances for Axiom A flows, with Long Jin, to appear in Communications in Mathematical Physics.
The fractal uncertainty principle via Dolgopyat's method in higher dimensions, with Aidan Backus and James Leng, to appear in Analysis&PDE.
Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds, with Qiuyu Ren.
Localized initial data for Einstein equations, with Yuchen Mao.
Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces, with Qiuyu Ren.
Flat trace estimates for Anosov flows, with Long Jin, to appear in Mathematical Research Letters.
Exact control for Schrödinger equation on torus from small balls, Pure and Applied Analysis 3(2021), 387-401.
On 0-th order pseudodifferential operator on the circle, Proceedings of the AMS, 152(2024), no.8, 3289–3297.
Selected Talks
- Dirac cones and magic angles in the Bistritzer–MacDonald TBG Hamiltonian, Roscoff workshop on 2D and moiré materials, Roscoff, July 2024.
- Optimal enhanced dissipation for contact Anosov flows, Oberwolfach, November 2023;
- Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds, PDE/Analysis seminar, MIT, May 2023.
- Fractal uncertainty principle via Dolgopyat's method in higher dimensions, Group actions seminar, UCSD, April 2023.
Teaching
Fall 2024: Directed Reading Program with Jiaqi Hao on microlocal analysis.
Spring 2022: Directed Reading Program with Troy Tsubota on differentiable manifolds.
Fall 2021: Math 53 Multivariable Calculus.
Spring 2021: Math 53 Multivariable Calculus.
Fall 2020: Directed Reading Program with Ayush Kamat on measure theory.
Notes
Notes on random perturbation of non-self-adjoint operators, taken from the topics course in Spring 2021 taught by Maciej Zworski.
Seminar
I organized a learning seminar on fractal uncartainty principle in January, 2022.
I organized a learning seminar on semiclassical analysis in spring 2022.
I co-organized Harmonic Analysis and Differential Equations Seminar (HADES) with Yonah Borns-Weil and Izak Oltman from fall 2022 to spring 2023.
I co-organized a learning seminar on orbit method for automorphic forms in fall 2023 with Christopher Dowd and Seewoo Lee.
